Question

The diagram represents a flower border that is 3 feet wide surrounding a rectangular sitting area. Write an expression in factored form that represents the area of the flower border.

Answer 1

Answer:

6(3x+11)

Explanation:

the length of the flower field is 3x+3+3, which is 3x+6

the height is 3+5+3, which is 11

the expression for the flower area is 11(3x+6)

since we are only supposed to be looking for the flowering field, we subtract the sitting area.

11(3x+6) - 3x*5

simplify. 33x + 66 - 15x

simplify. 18x + 66

factor. 6(3x + 11)

Answer 2

3* (36 - 5x)

Explanation:

The total area of the flower garden is equal to the surface of the rectangle that encloses the flowers border and the sitting area minus the area of the sitting area.

Rectangle area

Three flower segments height ---- 9 feet

4 flower segments length ----------- 12 feet

Rectangle area = 12*9 ft^2 = 108 ft^2

Sitting area

Sitting area = 3x*5 = 15x

Area of the flower border (A_flwb)

A_flwb = 108 ft^2 - 15x = 3* (36 - 5x)